Bubble-based EMMS

From the above derivation, we can see that the SFM may revert to the cluster-based EMMS or bubble-based EMMS hydrodynamic models under different assumptions of structure parameters. Thus, SFM unifies these models. Indeed, the mesoscale structure has always been the critical part of the EMMS model. We may expect more variants of the EMMS model wiU be proposed because of different descriptions of the mesoscale structure (Hong et al, 2013). 

Shi Z, Wang W, Li J A bubble-based EMMS model for gas-sohd bubbhng fluidization,... 

Here, Pc is the mixture density of the dense phase. U up i is defined by J Uf-U/), where Uf and U are mean velocities of the dilute and dense phases, respectively. This definition of mesoscale slip velocity differs a little bit from that in the cluster-based EMMS model, because the continuous phase transforms from the dilute phase to the dense phase. And their quantitative difference is l-f)PgUgc/Pc, which is normally negligible for gas-solid systems. Similarly, the closure of Fdi switches to the determination of bubble diameter. And it is well documented in literature ever since the classic work of Davidson and Harrison (1963). Compared to cluster diameter, bubble diameter arouses less disputes and hence is easier to characterize. The visual bubbles are normally irregular and in constantly dynamic transformation, which may deviate much from spherical assumption. Thus, the diameter of bubble here can also be viewed as drag-equivalent definition. 

Liu X, Jiang Y, Liu C, Wang W, Li J Hydrodynamic modeling of gas—solid bubbling fluidization based on energy-minimization multiscale (EMMS) theory, Ind Eng Chem Res 53 2800-2810, 2014. 

Exchange between large and small bubbles (bubble coalescence / breakup) Exchange between large and small bubbles (bubble shrinkage / expansion) Figure 13 A reactor model based on the EMMS approach. Reprinted from Jiang et al (2015) with permission from Elsevier. 

---